ENH: use np.hypot for standard.magnitude

[DWesl]

np.hypot finds the length of the hypotenuse of a right triangle with leg lengths given by the arguments.

The main benefit here would likely be locality (which should boost speed a bit): hypot would perform one pass through each array (two total) instead of the current four. NumPy also tries to avoid over- and under-flow, but that's less of a concern if people pass winds mostly in the 0.1 m/s - 100 m/s range.

There might also be a small speed boost from using sqrt and square functions instead of a general power function, but I suspect this particular function is usually memory-limited, especially given the emphasis on SIMD in recent NumPy development.

[ajdawson]

Is numpy/numpy#14761 no longer accurate, or are you just assuming performance benefits from this?

[DWesl]

Good catch. It was an assumption, but a quick test suggests that's still accurate for "small" arrays (less than a million elements; around 16 levels on a one-degree grid):

$ python -m timeit -s 'import numpy as np; arr1 = np.arange(1_000_000, dtype="f4"); arr2 = np.ones_like(arr1)' \
>    '(arr1 ** 2 + arr2 ** 2) ** 0.5'
100 loops, best of 5: 3.19 msec per loop
$ python -m timeit -s 'import numpy as np; arr1 = np.arange(1_000_000, dtype="f4"); arr2 = np.ones_like(arr1)' \
>    'np.sqrt(arr1 ** 2 + arr2 ** 2)'
100 loops, best of 5: 3.32 msec per loop
$ python -m timeit -s 'import numpy as np; arr1 = np.arange(1_000_000, dtype="f4"); arr2 = np.ones_like(arr1)' \
>    'np.hypot(arr1, arr2)'
100 loops, best of 5: 3.83 msec per loop
$ python -m timeit -s 'import numpy as np; arr1 = np.arange(1_000_000, dtype="f4"); arr2 = np.ones_like(arr1)' \ 
>    '(arr1 * arr2 + arr2 * arr2) ** 0.5'
100 loops, best of 5: 3.35 msec per loop

but that changes for "large" arrays (over ten million elements; around 10 levels on a quarter-degree grid):

$ python -m timeit -s 'import numpy as np; arr1 = np.arange(10_000_000, dtype="f4"); arr2 = np.ones_like(arr1)' \
>     '(arr1 ** 2 + arr2 ** 2) ** 0.5'
5 loops, best of 5: 70.9 msec per loop
$ python -m timeit -s 'import numpy as np; arr1 = np.arange(10_000_000, dtype="f4"); arr2 = np.ones_like(arr1)' \
>     'np.sqrt(arr1 ** 2 + arr2 ** 2)'
5 loops, best of 5: 68.3 msec per loop
$ python -m timeit -s 'import numpy as np; arr1 = np.arange(10_000_000, dtype="f4"); arr2 = np.ones_like(arr1)' \
>     'np.hypot(arr1, arr2)'
5 loops, best of 5: 52.6 msec per loop
$ python -m timeit -s 'import numpy as np; arr1 = np.arange(10_000_000, dtype="f4"); arr2 = np.ones_like(arr1)' \
>     'np.sqrt(arr1 * arr1 + arr2 * arr2)'
5 loops, best of 5: 68.6 msec per loop

I'd forgotten the extra conditionals in hypot, but I still think locality will win out ... eventually. It looks like that won't happen until there's at least a gigabyte of data, which seems to be rather a lot, and users can always call it themselves if they have enough data that it would help.